PHYS 3202 Classical Mechanics II  Homework #8
Due at 12:05pm, Friday April 8, 2011 in the class
Please show intermediate steps of your calculations.
Problem 1
(10 points): Calculate the inertia tensor of a system of four point
like objects with mass
m
each, connected by rigid massless rods to form a regular
tetrahedron (
http://en.wikipedia.org/wiki/Tetrahedron
). The length of each
edge is
a
. The total mass of the system is 4
m
. The coordinates of the four masses
can be given as
(+
a
√
3
,
0
,

a
2
√
6
);
(

a
2
√
3
,
+
a
2
,

a
2
√
6
);
(

a
2
√
3
,

a
2
,

a
2
√
6
);
(0
,
0
,
+
r
3
8
a
)
.
You may give calculation details for one diagonal element and one offdiagonal ele
ment of the inertia tensor, and simply list final answers for all remaining 7 elements.
Problem 2
(10 points): Which of the following matrices can NOT represent an
inertia tensor? Give your reasoning for each.
c
is a positive constant.
c
1
1
0
2
2
0
0
0
2
;
c
1
0
0
0
1
0
0
0
3
;
c
3
4
0
4
5
0
0
0
3
.
(1)
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 Spring '11
 Tan
 mechanics, Angular Momentum, Inertia, Mass, Work, 4m, θ, Thornton, Marion

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